Problems on Profit Loss
Q21. A company offers three types of successive discounts. 1st 20% and 10% ; 2nd 15% and 15%, 3rd 25 % and 5%. Which offer is better for a customer ?
(a) 1st
(b) 2nd
(c) 3rd
(d) All are equal
Answer: (c) 3rd
Let the M.P be Rs. 100
1st payment = 80% of 90% of Rs. 100
= | 80 | X | 90 | X 100 |
100 | 100 |
= Rs. 72
2nd payment = 85% of 85% of Rs. 100
= | 85 | X | 85 | X 100 |
100 | 100 |
= Rs. 72.25
3rd payment = 75% of 95% of Rs. 100
= | 75 | X | 95 | X 100 |
100 | 100 |
= Rs. 71.25
∴ 3rd payment is better
Q22. A discount series of P% and Q% on an invoice is the same as a single discount of
(a) (p - q + | pq | )% |
100 |
(b) {(p + q) - | pq | }% |
100 |
(c) [100 - (p + q + | pq | )]% |
100 |
(d) [100 - (p - q + | pq | )]% |
100 |
Answer:
(b) {(p + q) - | pq | }% |
100 |
Let the M.P be Rs. 100, then
S.P = (100 - p)% of (100 - q)% of Rs. 100
= Rs. { | 100 - p | X | 100 - q | X 100 } = Rs. | (100 - p) (100 - q) |
100 | 100 | 100 |
Single discount = { 100 - | (100 - p) (100 - q) | } % |
100 |
= [ | 1000 - { 1000 - 100q - 100p + pq} | ] % |
100 |
= | 100q + 100p - pq |
100 |
= { (p + q) - | pq | }% |
100 |
Q23. A retailer allows a trade discount of 10% on the cost. By how much above the cost should the product be labelled for sale to gain 18%.
(a) 31%
(b) 31(1/9)%
(c) 35%
(d) 35(1/3)%
Answer: (b) 31(1/9)%
Let the C.P be Rs. 100 and let the M.P be Rs. x above Rs. 100
Then M.P = Rs. (100+x) and discount = 10%
∴ S.P = | 90 | X (100 + x) = Rs. | 9 (100 + x) |
100 | 10 |
∴ | 9 (100 + x) | = 118 |
10 |
⇒ 100 + x = | 118 X 10 |
9 |
∴ x = | 1180 | - 100 |
9 |
= | 1180 - 900 | = | 280 |
9 |
= 31 | 1 | % |
9 |
∴ Cost should be labelled at 31(1/9)% above C.P
Q24. A shopkeeper gives two sucessive discounts on an article marked Rs. 600. The first discount given is 10%. If the customer pays Rs. 459 for the article, the second discount given is
(a) 10%
(b) 12%
(c) 13%
(d) 15%
Answer: (d) 15%
Let the second discount be x%
∴ 90% of (100 - x)% of Rs. 600 = Rs. 459
⇒ | 90 | X | 100 - x | X 600 = 459 |
100 | 100 |
⇒ | 27 (100 -x) | = 459 |
5 |
⇒ 100 - x = | 459 X 5 |
27 |
⇒ 100 - x = 85
⇒ x = 100 - 85 = 15 %
Q25. A shopkeeper sold an air-conditioner for Rs. 25938 with a discount of 10% and earned a profit of 4%. What would have been the percentage of profit earned if no discount were offered.
(a) 13.21%
(b) 15.55%
(c) 17.20%
(d) 22.85%
Answer: (b) 15.55%
Let the M.P be Rs. x
∴ x X (90/100) = 25938
⇒ x = (25938 X 10)/9 = 28820
∴ M.P = Rs. 28820
S.P = Rs. 25938
Profit = 4%
∴ C.P = (100/104) X 25938 = Rs. 24940.38
New S.P = Rs. 28820
C.P = Rs. 24940.38
∴ Profit = Rs (28820 - 24940.38) = Rs. 3879.62
Profit % = (3879.62/24940.38) X 100 = 15.55%
Q26. A trader marks his goods at such a price that he can deduct 10% for cash and yet make 20% profit. The marked price of an item which cost him Rs. 90.
(a) Rs. 120
(b) Rs. 130
(c) Rs. 135
(d) Rs. 145
Answer: (a) Rs. 120
C.P = Rs. 90
Gain % = 20%
S.P = Rs. (120/100) X 90 = Rs. 108
Let M.P be Rs. x
Now 90% of x = 108
⇒ (90/100) X x = 108
⇒ x = (10800/90) = 120
∴ M.P = Rs. 120
Q27. A dealer buys an article marked at Rs. 24000 with 20% and 5% off. He spends Rs. 1000 on its repairs and sells it for Rs. 24000. What is his gain or loss percent ?
(a) 18.15 %
(b) 22.31 %
(c) 24.74 %
(d) 29.25 %
Answer: (c) 24.74 %
C.P = {80% of 95% of Rs. 24000} + 1000
= | 80 | X | 95 | X 24000 + 1000 |
100 | 100 |
= Rs. (18240 + 1000)
= Rs. 19240
S.P = Rs. 24000
∴ Profit = Rs. (24000 - 19240) = Rs. 4760
∴ Profit % = (4760 / 19240) X 100 = 24.74 %
Q28. An article is listed at Rs. 800 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or loss, if he gives a single discount of 16% instead of two dicounts ?
(a) Rs. 5.12
(b) Rs. 6.50
(c) Rs. 11.25
(d) Rs. 15
Answer: (a) Rs. 5.12
In 1st case
S.P = 92% of 92% of Rs. 800
= | 92 | X | 92 | X 800 |
100 | 100 |
= Rs. 677.12
In 2nd case,
S.P = 84% of Rs. 800
= (84/100) X 800
= Rs. 672
Loss = Rs. (677.12 - 672) = Rs. 5.12
Q29. A tradesman gives 4% discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35%. The marked price is increased above the cost price by
(a) 29%
(b) 37%
(c) 42%
(d) 50%
Answer: (d) 50%
Let, the C.P of each article be Rs. x
C.P of 16 article be Rs. 16x
S.P of 15 articles = 135% of Rs. 16x
= Rs. (135/100) X 16x = Rs. (108x/5)
S.P of 1 article = Rs. ( | 108x | X | 1 | ) = Rs. | 36x |
5 | 15 | 25 |
If S.P is Rs. 96, M.P = Rs. 100
S.P is Rs. (36x/25), M.P = Rs. ( | 100 | X | 36x | ) = Rs. | 3x |
96 | 25 | 2 |
Increase in M.P over C.P = Rs. ( | x | X | 1 | X 100 )% = 50% |
2 | x |
Q30. A trader wishes to gain 20% after allowing 10% discount on the marked price to his customers. At what percent higher than the cost price must he mark his goods ?
(a) 19(1/3)%
(b) 26(1/4)%
(c) 27(1/4)%
(d) 33(1/3)%
Answer: (d) 33(1/3)%
Let, the C.P be Rs. 100
Let the M.P be Rs. x above Rs. 100
∴ S.P = Rs. [ | 90 | X (100 + x)] = Rs. [ | 9 (100 + x) | ] |
100 | 10 |
∴ | 9(100 + x) | = 120 |
10 |
⇒ 9 (100 + x) = 1200
⇒ 9x = 1200 - 900
⇒ x = (300 / 9) = 33 (1/3)
∴ Cost should be labelled at 33(1/3)% higher than C.P
Practice Test Exam